genpoly computes the unique polynomial  over  from the integer n with coefficients less than  in magnitude such that  .

This is directly related to b-adic expansion of an integer. If the base-b representation of the integer n is  where  are integers modulo b (using symmetric representation) then the polynomial generated is .

If n is a polynomial with integer coefficients then each integer coefficient is expanded into a polynomial.  This polynomial, n, must be in fully expanded form.

The genpoly command is thread-safe as of Maple 15.

For more information on thread safety, see index/threadsafe.